non-Fermi Liquid Ground State Research Articles

Two-stage superconductivity in the Hatsugai–Kohomoto-BCS model

Superconductivity in strongly correlated electrons can emerge out from a normal state that is beyond the Landau’s Fermi liquid paradigm, often dubbed as ‘non-Fermi liquid’. While the theory for non-Fermi liquid is still not yet conclusive, a recent study on the exactly-solvable Hatsugai–Kohomoto (HK) model has suggested a non-Fermi liquid ground state whose Green’s function resembles the Yang–Rice–Zhang ansatz for cuprates (2020 Phillips et al Nat. Phys. 16 1175). Similar to the effect of on-site Coulomb repulsion in the Hubbard model, the repulsive interaction in the HK model divides the momentum space into three parts: empty, single-occupied and double-occupied regions, that are separated from each other by two distinct Fermi surfaces. In the presence of an additional Bardeen–Cooper–Schrieffer-type pairing interaction of a moderate strength, we show that the system exhibits a ‘two-stage superconductivity’ feature as temperature decreases: a first-order superconducting transition occurs at a temperature T c that is followed by a sudden increase of the superconducting order parameter at a lower temperature . At the first stage, , the pairing function arises and the entropy is released only in the vicinity of the two Fermi surfaces; while at the second stage, , the pairing function becomes significant and the entropy is further released in deep (single-occupied) region in the Fermi sea. The phase transitions are analyzed within the Ginzburg–Landau theory. Our work sheds new light on unconventional superconductivity in strongly correlated electrons.

Mixed-valent metallic pyrochlore iridate: A possible route to non-Fermi liquids

Non-Fermi liquid behavior in some fermionic systems has attracted significant interest in last few decades. Certain pyrochlore iridates with stronger spin-orbit coupling strength have recently been added to the list. Here, we provide evidence of such a non-Fermi liquid ground state in another mixed-valent metallic pyrochlore iridate ${\mathrm{Pb}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$, through the combined investigation of electronic, magnetic, and thermodynamic properties as a function of temperature ($T$) and applied magnetic field ($H$). Resistivity measurement showed a linear temperature dependence down to 15 K below which it shows $\ensuremath{\rho}\ensuremath{\sim}{T}^{3/2}$ dependence while magnetic susceptibility diverges as $\ensuremath{\chi}(T$) $\ensuremath{\sim}{T}^{\ensuremath{-}\ensuremath{\alpha}}$ ($\ensuremath{\alpha}<1$) below 10 K. While a strong negative ${\mathrm{\ensuremath{\Theta}}}_{\text{CW}}$ has been observed from Curie-Weiss fitting, the absence of any long-range order down to 80 mK only indicates the presence of strong inherent geometric frustration in the system. Heat capacity data showed ${C}_{p}\ensuremath{\sim}Tln({T}_{0}/T)+\ensuremath{\beta}{T}^{3}$ dependence below 15 K down to 1.8 K. More importantly spin-orbit coupling strength by x-ray absorption spectroscopy was found to be weaker in ${\mathrm{Pb}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ compared to other pyrochlore iridates. In the absence of any large moment rare earth magnetic ion, ${\mathrm{Pb}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ presents a rare example of an iridate system showing non-Fermi liquid behavior due to disordered distribution of ${\mathrm{Ir}}^{4+}$ and ${\mathrm{Ir}}^{5+}$ having markedly different strengths of spin-orbit coupling which might offer a prescription for achieving new non-Fermi liquid systems.

Nontrivial fixed points and truncated SU(4) Kondo models in a quasi-quartet multipolar quantum impurity problem

The multipolar Kondo problem, wherein the quantum impurity carries higher-rank multipolar moments, has seen recent theoretical and experimental interest due to proposals of novel non-Fermi liquid states and the availability of a variety of material platforms. The multipolar nature of local moments, in conjunction with constraining crystal field symmetries, leads to a vast array of possible interactions and resulting non-Fermi liquid ground states. Previous works on Kondo physics have typically focused on impurities that have two degenerate internal states. In this work, inspired by recent experiments on the tetragonal material ${\mathrm{YbRu}}_{2}{\mathrm{Ge}}_{2}$, which has been shown to exhibit a local moment with a quasi-fourfold degenerate ground state, we consider the Kondo effect for such a quasi-quartet multipolar impurity. In the tetragonal crystal field environment, the local moment supports dipolar, quadrupolar, and octupolar moments, which interact with conduction electrons in entangled spin and orbital states. Using renormalization group analysis, we uncover a number of emergent quantum ground states characterized by nontrivial fixed points. It is shown that these previously unidentified fixed points are described by truncated SU(4) Kondo models, where only some of the SU(4) generators (representing the impurity degrees of freedom) are coupled to conduction electrons. Such novel nontrivial fixed points are unique to the quasi-quartet multipolar impurity, reinforcing the idea that an unexplored rich diversity of phenomena may be produced by multipolar quantum impurity systems.

Rényi entanglement entropy of Fermi and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories

We present a new method for calculating Renyi entanglement entropies for fermionic field-theories originating from microscopic Hamiltonians. The method builds on an operator identity which we discover for the first time. The identity leads to the representation of traces of operator products, and thus Renyi entropies of a subsystem, in terms of fermionic-displacement operators. This allows for a very transparent path-integral formulation, both in and out-of-equilibrium, having a simple boundary condition on the fermionic fields. The method is validated by reproducing well known expressions for entanglement entropy in terms of the correlation matrix for non-interacting fermions. We demonstrate the effectiveness of the method by explicitly formulating the field theory for Renyi entropy in a few zero and higher-dimensional large-$N$ interacting models based on the Sachdev-Ye-Kitaev (SYK) model, and for the Hubbard model within dynamical mean-field theory (DMFT) approximation. We use the formulation to compute Renyi entanglement entropy of interacting Fermi liquid (FL) and non-Fermi liquid (NFL) states in the large-$N$ models and compare successfully with the results obtained via exact diagonalization for finite $N$. We elucidate the connection between entanglement entropy and residual entropy of the NFL ground state in the SYK model and extract sharp signatures of quantum phase transition in the entanglement entropy across an NFL to FL transition. Furthermore, we employ the method to obtain nontrivial system-size scaling of entanglement in an interacting diffusive metal described by a chain of SYK dots.

Quantum fluctuations in the quasi-one-dimensional non-Fermi liquid system CeCo2Ga8 investigated using μSR

Reduced dimensionality offers a crucial information in deciding the type of the quantum ground state in heavy fermion materials. Here we have examined stoichiometric CeCo$_{2}$Ga$_{8}$ compound, which crystallizes in a quasi-one-dimensional crystal structure with Ga-Ce-Co chains along the $c$-axis. The low-temperature behavior of magnetic susceptibility ($\chi\sim-\ln T$), heat capacity ($C_p/T\sim-\ln T$), and resistivity ($\rho\sim T^{n}$) firmly confirm the non-Fermi liquid ground state of CeCo$_{2}$Ga$_{8}$. We studied the low-energy spin dynamics of CeCo$_{2}$Ga$_{8}$ compound utilizing zero field (ZF-) and longitudinal field (LF-) muon spin relaxation ($\mu$SR) measurements. ZF-$\mu$SR measurement reveals the absence of long-range magnetic ordering down to 70 mK, and interestingly below 1 K, the electronic relaxation rate sharply rises, intimating the appearance of low energy quantum spin fluctuations in CeCo$_{2}$Ga$_{8}$.

Parafermionic generalization of the topological Kondo effect

We propose and study a parafermionic generalization of the topological Kondo effect. The latter has been predicted to arise for a Coulomb-blockaded mesoscopic topological superconductor (Majorana box), where at least three normal leads are tunnel-coupled to different Majorana zero modes on the box. The Majorana states represent a quantum impurity spin that is partially screened due to cotunneling processes between leads, with a stable non-Fermi liquid ground state. Our theory studies a generalization where (i) Majorana states are replaced by topologically protected parafermionic zero modes, (ii) charging effects again define a spin-like quantum impurity on the resulting parafermion box, and (iii) normal leads are substituted by fractional edge states. In this multi-terminal problem, different fractional edge leads couple only via the parafermion box. We show that although the linear conductance tensor exhibits similar behavior as in the Majorana case, both at weak and strong coupling, our parafermionic generalization is actually not a Kondo problem but defines a rich new class of quantum impurity problems. At the strong-coupling fixed point, a current injected through a reference lead will be isotropically partitioned into outgoing currents in all other leads, together with a universal negative current scattered into the reference lead. The device can thus be operated as current extractor, where the current partitioning is noiseless at the fixed point. We describe a fractional quantum Hall setup proximitized by superconductors and ferromagnets, which could allow for an experimental realization in the near future.

Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals

We illuminate the intriguing role played by spatial anisotropy in three-dimensional Luttinger semimetals featuring quadratic band touching and long-range Coulomb interactions. We observe the anisotropy to be subject to an exceptionally slow renormalization group (RG) evolution so that it can be considered approximately constant when computing the impact of quantum fluctuations on the remaining couplings of the system. Using perturbative RG we then study the competition of all local short-range interactions that are generated from the long-range interactions for fixed anisotropy. Two main effects come to light for sufficiently strong anisotropy. First, the three-dimensional system features an Abrikosov non-Fermi liquid ground state. Second, there appear qualitatively new fixed points which describe quantum phase transitions into phases with nemagnetic orders - higher-rank tensor orders that break time-reversal symmetry, and thus have both nematic and magnetic character. In real materials these phases may be realized through sufficiently strong microscopic short-range interactions. On the pyrochlore lattice, the anisotropy-induced fixed points determine the onset of all-in-all-out or spin ice ordering of local magnetic moments of the electrons.

Bulk superconductivity at 84 K in the strongly overdoped regime of cuprates

By means of magnetization, specific heat and muon-spin relaxation measurements, we investigate high-pressure oxidized \mohpo, in which overdoping is achieved up to $p \sim 0.45$ hole/Cu, well beyond the $T_c - p$ superconducting dome of cuprates, where Fermi liquid behavior is expected. Surprisingly, we find bulk superconductivity with $T_c$=84 K and superfluid density similar to those of optimally doped Y123. On the other hand, specific heat data display a large electronic contribution at low temperature, comparable to that of nonsuperconducting overdoped La214. These results point at an unusual high-$T_c$ phase with a large fraction of unpaired holes. Further experiments may assess the Fermi liquid properties of the present phase, which would put into question the paradigm that the high $T_c$ of cuprates originates from a non-Fermi liquid ground state.

Competing Kondo Effects in Non-Kramers Doublet Systems

In non-Kramers Kondo systems with a quadrupolar degrees of freedom, an ordinary magnetic Kondo effect can compete with the quadrupolar Kondo effect. We discuss such competition keeping Pr$T_{2}$Zn$_{20}$ ($T$=Ir, Rh) and Pr$T_{2}$Al$_{20}$ ($T$=V, Ti) in mind, where the $\Gamma_{3}$ non-Kramers crystalline-electric-field (CEF) doublet ground state is realized in Pr$^{3+}$ ion with $(4f)^{2}$ configuration under cubic symmetry. The quadrupolar Kondo effect can be described by the two-channel Kondo model, which leads to the local non-Fermi-liquid (NFL) ground state, while the magnetic Kondo effect favors the ordinary local Fermi-liquid (FL) ground state. Based on the minimal extended two-channel Kondo model including the magnetic Kondo coupling as well, we investigate the competition and resulting thermodynamics, and orbital/magnetic, and single-particle excitation spectra by the Wilson's numerical renormalization-group (NRG) method. There exists the first-order transition between the NFL and FL ground states. In addition to these two states, the alternative FL state accompanied by a free magnetic spin appears in intermediate temperature range, which eventually reaches the true NFL ground state, as a consequence of stronger competition between the magnetic and quadrupolar Kondo effects. In this peculiar state, the magnetic susceptibility shows a Curie-like behavior, while the orbital fluctuation exhibits the FL behavior. Moreover, the single-particle spectra yield a more singular behavior. Implications to the Pr 1-2-20 systems are briefly discussed.

Construction of a non-Fermi liquid ground state

Construction of a non-Fermi liquid ground state

Quantum critical scaling at the edge of Fermi liquid stability in a cuprate superconductor

In the high-temperature cuprate superconductors, the pervasiveness of anomalous electronic transport properties suggests that violation of conventional Fermi liquid behavior is closely tied to superconductivity. In other classes of unconventional superconductors, atypical transport is well correlated with proximity to a quantum critical point, but the relative importance of quantum criticality in the cuprates remains uncertain. Here, we identify quantum critical scaling in the electron-doped cuprate material La(2-x)Ce(x)CuO(4) with a line of quantum critical points that surrounds the superconducting phase as a function of magnetic field and charge doping. This zero-temperature phase boundary, which delineates a metallic Fermi liquid regime from an extended non-Fermi liquid ground state, closely follows the upper critical field of the overdoped superconducting phase and gives rise to an expanse of distinct non-Fermi liquid behavior at finite temperatures. Together with signatures of two distinct flavors of quantum fluctuations, these facts suggest that quantum criticality plays a significant role in shaping the anomalous properties of the cuprate phase diagram.

Local Quantum Criticality of an Iron-Pnictide Tetrahedron

Motivated by the close correlation between transition temperature (T(c)) and the tetrahedral bond angle of the As-Fe-As layer observed in the iron-based superconductors, we study the interplay between spin and orbital physics of an isolated iron-arsenide tetrahedron embedded in a metallic environment. Whereas the spin-Kondo effect is suppressed to low temperatures by Hund's coupling, the orbital degrees of freedom are expected to quantum mechanically quench at high temperatures, giving rise to an overscreened, non-Fermi liquid ground state. Translated into a dense environment, this critical state may play an important role in the superconductivity of these materials.

UnconventionalT−HPhase Diagram in the Noncentrosymmetric CompoundYb2Fe12P7

The temperature-(T-)magnetic-field (H) phase diagram for the noncentrosymmetric compound Yb(2)Fe(12)P(7), [corrected] determined from electrical resistivity (ρ), specific heat (C), and magnetization (M) measurements on single crystal specimens, is reported. This system exhibits a crossover from a magnetically ordered non-Fermi-liquid (NFL) phase at low H to another NFL phase at higher H. The crossover occurs near the value of H where the magnetic ordering temperature (T(M)) is no longer observable in C(T,H)/T and ρ(T,H), but not where T(M) extrapolates smoothly to T=0 K at a possible quantum critical point (QCP). This indicates the occurrence of a quantum phase transition between the two NFL phases. The lack of a clear relationship between the extrapolated QCP and NFL behavior suggests an unconventional route to the NFL ground states.

Apparent Violation of the Wiedemann-Franz Law near a Magnetic Field Tuned Metal-Antiferromagnetic Quantum Critical Point

The temperature dependences of the interlayer electrical and thermal resistivity in a layered metal are calculated for Fermi liquid quasiparticles which are scattered inelastically by two-dimensional antiferromagnetic spin fluctuations. Both resistivities have a linear temperature dependence over a broad temperature range. Extrapolations to zero temperature made from this linear-T range give values that appear to violate the Wiedemann-Franz law. However, below a low-temperature scale, which becomes small close to the critical point, a recovery of this law occurs. Our results describe recent measurements on CeCoIn5 near a magnetic field-induced quantum phase transition. Hence, the experiments do not necessarily imply a non-Fermi liquid ground state.

Thermoelectric Transport through a Quantum Dot Coupled to a Normal Metal and BCS Superconductor

We discuss thermoelectric properties of a quantum dot coupled to one normal and one superconducting lead in the presence of the Kondo efiect and the Andreev scattering. We will focus on conductance, thermal conductance, thermopower and related quantities like thermoelectric flgure of merit which is a direct measure of the usefulness of the system for applications and the Wiedemann{Franz ratio which indicates if the system is in the Fermi liquid state. We will show that the superconductivity strongly modifles the thermal properties of the system. In particular, the thermopower is strongly enhanced near the superconducting transition temperature. Moreover, the Andreev re∞ections are suppressed due to strong on-dot Coulomb repulsion. The suppression of the Andreev re∞ections leads to a violation of the Wiedemann{Franz law and to a non-Fermi liquid ground state.

Interplay between spin-glass-like and non-Fermi-liquid behavior inCeNi1−xRhxSn

The effect of doping in CeNiSn has been studied by measurements of electrical resistivity, magnetic susceptibility, and specific heat for polycrystalline samples of ${\text{CeNi}}_{1\ensuremath{-}x}{\text{Rh}}_{x}\text{Sn}$. It was observed that the semimetallic compound CeNiSn transforms into a Kondo semiconductor upon the substitution of 2% of Rh for Ni. We show that the narrow Kondo-insulator gap formation can be associated with disorder-induced $f$-electron localization. The magnetic properties of the system gradually evolve from magnetic glassy state, observed for $0<x<0.08$, to non-Fermi-liquid (NFL) behavior, when the Rh doping increases. The series of ${\text{CeNi}}_{1\ensuremath{-}x}{\text{Rh}}_{x}\text{Sn}$ exhibits NFL behavior in the vicinity of a zero-temperature magnetic phase transition, which is associated with spin-glass-like ordering due to chemical substitution. The detailed investigations of magnetic properties with decreasing Rh concentration suggest an interplay between the spin-glass-like (glassy state) and NFL ground states for the concentration region $x<0.08$. On the basis of the experimental results, we propose a schematic phase diagram on the $T\ensuremath{-}x$ plane and demonstrate the rationale for the existence of a quantum critical point at ${x}_{c}\ensuremath{\approx}0.08$.

T-J Model Then and Now: a Personal Perspective from the Pioneering Times

In this overview I sketch briefly the path to the so-called {\em t-J model} derived for the first time 30 years ago and provide its original meaning within the theory of strongly correlated magnetic metals with a non-Fermi (non-Landau) liquid ground state. An emergence of the concept of {\em real space pairing}, is discussed in a historical prospective. A generalization of this model to the many-orbital situation is briefly discussed. The emphasis is put on didactical exposition of ideas, as they were transformed into mathematical language. The concept of {\em hybrid pairing} is introduced in the same context at the end.

Interplay between spin-glass and non-Fermi-liquid behavior inY1−xUxPd3

We report the results of a study of the ac and dc magnetic susceptibilities of ${\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{U}}_{x}{\mathrm{Pd}}_{3}$. The magnetic properties of the system gradually evolve from the spin-glass (SG) behavior observed for $x=0.4$ to the non-Fermi-liquid (NFL) ground state that develops at $x=0.2$. For $x=0.4$, the SG properties are remarkably similar to those found in canonical spin glasses. We have been able to analyze our data in terms of critical slowing down when $T$ approaches the critical temperature associated with a spin-glass freezing phase transition. The values obtained for the dynamic and static critical exponents [$z\ensuremath{\nu}=10\ifmmode\pm\else\textpm\fi{}1$, $\ensuremath{\beta}=0.9(1)$, $\ensuremath{\gamma}=1.8(2)$] support the existence of a true spin-glass phase transition in ${\mathrm{Y}}_{0.6}{\mathrm{U}}_{0.4}{\mathrm{Pd}}_{3}$. On the other hand, the evolution of magnetic properties with a decreasing U concentration suggests an interplay between the SG and NFL ground states. The ground state that finally appears for $x=0.2$ displays a temperature dependence of its low-field ac susceptibility consistent with the prediction of the Griffith's phase model of NFL behavior. The role played by compositional disorder in the development of the NFL state is discussed.

Can Competition between the Crystal Field and the Kondo Effect Cause Non-Fermi-Liquid-Like Behavior?

The recently reported unusual behavior of the static and dynamical magnetic susceptibility as well as the specific heat in Ce(1-x)La(x)Ni9Ge4 has raised the question of a possible non-Fermi-liquid ground state in this material. We argue that for a consistent physical picture the crystal-field splitting of two low-lying magnetic doublets of the Ce 4f-shell must be taken into account. Furthermore, we show that for a splitting of the order of the low temperature scale T* of the system a crossover behavior between an SU(4) and an SU(2) Kondo effect is found. The screening of the two doublets occurs on different temperature scales leading to a different behavior of the magnetic susceptibility and the specific heat at low temperatures. The experimentally accessible temperature regime down to 50 mK still lies in the extended crossover regime into a strong-coupling Fermi-liquid fixed point.

Coherent Kondo insulating and non-Fermi liquid ground states in CeRhSb 1−xSn x

We present the structural properties, the magnetic susceptibility, and the resistivity ρ data for CeRhSb 1− x Sn x . CeRhSb is a Kondo insulator with narrow energy gap of 2 T K = 13 K , whereas CeRhSn has a non-Fermi liquid ground state. In view of the contrasting behavior of CeRhSb and CeRhSn, we investigate the solid solutions CeRhSb 1− x Sn x . The system exhibits a variety of different ρ ( T ) dependencies at the low temperatures: activated behavior ρ = ρ 0 exp ( Δ / k B T ) for Sb-rich samples ( x ⩽ 0.1 ), ρ ∝ T 2 for x = 0.2 , which transform into the dependences ρ ∝ - ln T for x = 0.9 , and ρ ∝ T ε (where ε ≅ 1 ) for Sn-rich samples. The properties indicate an evolution from the Kondo lattice state to the non-Fermi liquid via a heavy-fermion phase.